LMFDB - Embedded newform 600.2.m.d.299.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 4x^{12} + 12x^{10} + 16x^{8} + 48x^{6} + 64x^{4} + 64x^{2} + 256 $ x^16 + x^14 + 4x^12 + 12x^10 + 16x^8 + 48x^6 + 64x^4 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.5
Root			$-0.842022 - 1.13622i$ of defining polynomial
Character	$\chi$	$=$	600.299
Dual form			600.2.m.d.299.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.842022 - 1.13622i) q^{2} +(0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(1.76833 - 1.69499i) q^{6} +3.64426 q^{7} +(2.66415 - 0.949886i) q^{8} +(-2.90455 + 0.750707i) q^{9} +O(q^{10})$	\(q+(-0.842022 - 1.13622i) q^{2} +(0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(1.76833 - 1.69499i) q^{6} +3.64426 q^{7} +(2.66415 - 0.949886i) q^{8} +(-2.90455 + 0.750707i) q^{9} -5.07403i q^{11} +(-3.41486 - 0.581998i) q^{12} +1.70594 q^{13} +(-3.06855 - 4.14069i) q^{14} +(-3.32256 - 2.22724i) q^{16} +4.08117 q^{17} +(3.29867 + 2.66811i) q^{18} +1.26422 q^{19} +(0.796108 + 6.26164i) q^{21} +(-5.76522 + 4.27244i) q^{22} +4.70066i q^{23} +(2.21411 + 4.37009i) q^{24} +(-1.43644 - 1.93832i) q^{26} +(-1.92439 - 4.82667i) q^{27} +(-2.12095 + 6.97311i) q^{28} +1.06377 q^{29} +4.86950i q^{31} +(0.267024 + 5.65055i) q^{32} +(8.71829 - 1.10845i) q^{33} +(-3.43644 - 4.63712i) q^{34} +(0.254006 - 5.99462i) q^{36} +7.56830 q^{37} +(-1.06450 - 1.43644i) q^{38} +(0.372671 + 2.93118i) q^{39} +1.50141i q^{41} +(6.44427 - 6.17700i) q^{42} -3.43644i q^{43} +(9.70888 + 2.95307i) q^{44} +(5.34099 - 3.95806i) q^{46} +10.9176i q^{47} +(3.10106 - 6.19543i) q^{48} +6.28066 q^{49} +(0.891553 + 7.01235i) q^{51} +(-0.992853 + 3.26422i) q^{52} -8.87288i q^{53} +(-3.86378 + 6.25070i) q^{54} +(9.70888 - 3.46163i) q^{56} +(0.276176 + 2.17221i) q^{57} +(-0.895716 - 1.20868i) q^{58} -0.788328i q^{59} +0.627594i q^{61} +(5.53283 - 4.10023i) q^{62} +(-10.5850 + 2.73578i) q^{63} +(6.19543 - 5.06128i) q^{64} +(-8.60043 - 8.97257i) q^{66} +4.18178i q^{67} +(-2.37523 + 7.80911i) q^{68} +(-8.07677 + 1.02688i) q^{69} -6.21689 q^{71} +(-7.02510 + 4.75900i) q^{72} +4.21689i q^{73} +(-6.37267 - 8.59926i) q^{74} +(-0.735776 + 2.41903i) q^{76} -18.4911i q^{77} +(3.01667 - 2.89155i) q^{78} +0.992853i q^{79} +(7.87288 - 4.36094i) q^{81} +(1.70594 - 1.26422i) q^{82} -7.72544 q^{83} +(-12.4447 - 2.12095i) q^{84} +(-3.90455 + 2.89356i) q^{86} +(0.232385 + 1.82779i) q^{87} +(-4.81975 - 13.5180i) q^{88} -11.5742i q^{89} +6.21689 q^{91} +(-8.99447 - 2.73578i) q^{92} +(-8.36687 + 1.06377i) q^{93} +(12.4048 - 9.19282i) q^{94} +(-9.65055 + 1.69320i) q^{96} -7.40133i q^{97} +(-5.28845 - 7.13622i) q^{98} +(3.80911 + 14.7378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) $ 16 * q - 2 * q^4 + 2 * q^6	$ 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.842022	−	1.13622i	−0.595399	−	0.803430i
$2$	−0.842022	−	1.13622i	−0.595399	−	0.803430i
$3$	0.218455	+	1.71822i	0.126125	+	0.992014i
$3$	0.218455	+	1.71822i	0.126125	+	0.992014i
$4$	−0.581998	+	1.91345i	−0.290999	+	0.956723i
$5$		0			0
$5$		0			0
$6$	1.76833	−	1.69499i	0.721919	−	0.691977i
$7$	3.64426			1.37740			0.688701	−	0.725045i	$-0.258181\pi$
$7$	3.64426			1.37740			0.688701	+	0.725045i	$0.258181\pi$
$8$	2.66415	−	0.949886i	0.941921	−	0.335835i
$9$	−2.90455	+	0.750707i	−0.968185	+	0.250236i
$10$		0			0
$11$		−	5.07403i		−	1.52988i	−0.644103	−	0.764938i	$-0.722769\pi$
$11$		−	5.07403i		−	1.52988i	0.644103	−	0.764938i	$-0.277231\pi$
$12$	−3.41486	−	0.581998i	−0.985786	−	0.168008i
$13$	1.70594			0.473142			0.236571	−	0.971614i	$-0.423976\pi$
$13$	1.70594			0.473142			0.236571	+	0.971614i	$0.423976\pi$
$14$	−3.06855	−	4.14069i	−0.820105	−	1.10665i
$15$		0			0
$16$	−3.32256	−	2.22724i	−0.830639	−	0.556811i
$17$	4.08117			0.989830			0.494915	−	0.868941i	$-0.335199\pi$
$17$	4.08117			0.989830			0.494915	+	0.868941i	$0.335199\pi$
$18$	3.29867	+	2.66811i	0.777504	+	0.628878i
$19$	1.26422			0.290033			0.145016	−	0.989429i	$-0.453676\pi$
$19$	1.26422			0.290033			0.145016	+	0.989429i	$0.453676\pi$
$20$		0			0
$21$	0.796108	+	6.26164i	0.173725	+	1.36640i
$22$	−5.76522	+	4.27244i	−1.22915	+	0.910888i
$23$			4.70066i			0.980156i	0.871679	+	0.490078i	$0.163032\pi$
$23$			4.70066i			0.980156i	−0.871679	+	0.490078i	$0.836968\pi$
$24$	2.21411	+	4.37009i	0.451953	+	0.892042i
$25$		0			0
$26$	−1.43644	−	1.93832i	−0.281709	−	0.380137i
$27$	−1.92439	−	4.82667i	−0.370350	−	0.928892i
$28$	−2.12095	+	6.97311i	−0.400823	+	1.31779i
$29$	1.06377			0.197537			0.0987683	−	0.995110i	$-0.468510\pi$
$29$	1.06377			0.197537			0.0987683	+	0.995110i	$0.468510\pi$
$30$		0			0
$31$			4.86950i			0.874588i	0.899318	+	0.437294i	$0.144063\pi$
$31$			4.86950i			0.874588i	−0.899318	+	0.437294i	$0.855937\pi$
$32$	0.267024	+	5.65055i	0.0472036	+	0.998885i
$33$	8.71829	−	1.10845i	1.51766	−	0.192956i
$34$	−3.43644	−	4.63712i	−0.589344	−	0.795259i
$35$		0			0
$36$	0.254006	−	5.99462i	0.0423344	−	0.999103i
$37$	7.56830			1.24422			0.622110	−	0.782930i	$-0.286276\pi$
$37$	7.56830			1.24422			0.622110	+	0.782930i	$0.286276\pi$
$38$	−1.06450	−	1.43644i	−0.172685	−	0.233021i
$39$	0.372671	+	2.93118i	0.0596751	+	0.469364i
$40$		0			0
$41$			1.50141i			0.234482i	0.993104	+	0.117241i	$0.0374049\pi$
$41$			1.50141i			0.234482i	−0.993104	+	0.117241i	$0.962595\pi$
$42$	6.44427	−	6.17700i	0.994373	−	0.953131i
$43$		−	3.43644i		−	0.524052i	−0.965061	−	0.262026i	$-0.915609\pi$
$43$		−	3.43644i		−	0.524052i	0.965061	−	0.262026i	$-0.0843906\pi$
$44$	9.70888	+	2.95307i	1.46367	+	0.445193i
$45$		0			0
$46$	5.34099	−	3.95806i	0.787486	−	0.583584i
$47$			10.9176i			1.59249i	0.604975	+	0.796245i	$0.293183\pi$
$47$			10.9176i			1.59249i	−0.604975	+	0.796245i	$0.706817\pi$
$48$	3.10106	−	6.19543i	0.447600	−	0.894234i
$49$	6.28066			0.897237
$50$		0			0
$51$	0.891553	+	7.01235i	0.124842	+	0.981926i
$52$	−0.992853	+	3.26422i	−0.137684	+	0.452666i
$53$		−	8.87288i		−	1.21878i	−0.792869	−	0.609392i	$-0.791414\pi$
$53$		−	8.87288i		−	1.21878i	0.792869	−	0.609392i	$-0.208586\pi$
$54$	−3.86378	+	6.25070i	−0.525794	+	0.850612i
$55$		0			0
$56$	9.70888	−	3.46163i	1.29740	−	0.462580i
$57$	0.276176	+	2.17221i	0.0365804	+	0.287717i
$58$	−0.895716	−	1.20868i	−0.117613	−	0.158707i
$59$		−	0.788328i		−	0.102632i	−0.998682	−	0.0513158i	$-0.983658\pi$
$59$		−	0.788328i		−	0.102632i	0.998682	−	0.0513158i	$-0.0163415\pi$
$60$		0			0
$61$			0.627594i			0.0803552i	0.999193	+	0.0401776i	$0.0127924\pi$
$61$			0.627594i			0.0803552i	−0.999193	+	0.0401776i	$0.987208\pi$
$62$	5.53283	−	4.10023i	0.702670	−	0.520730i
$63$	−10.5850	+	2.73578i	−1.33358	+	0.344675i
$64$	6.19543	−	5.06128i	0.774429	−	0.632661i
$65$		0			0
$66$	−8.60043	−	8.97257i	−1.05864	−	1.10445i
$67$			4.18178i			0.510886i	0.966824	+	0.255443i	$0.0822213\pi$
$67$			4.18178i			0.510886i	−0.966824	+	0.255443i	$0.917779\pi$
$68$	−2.37523	+	7.80911i	−0.288040	+	0.946994i
$69$	−8.07677	+	1.02688i	−0.972329	+	0.123622i
$70$		0			0
$71$	−6.21689			−0.737810			−0.368905	−	0.929467i	$-0.620267\pi$
$71$	−6.21689			−0.737810			−0.368905	+	0.929467i	$0.620267\pi$
$72$	−7.02510	+	4.75900i	−0.827915	+	0.560853i
$73$			4.21689i			0.493550i	0.969073	+	0.246775i	$0.0793709\pi$
$73$			4.21689i			0.493550i	−0.969073	+	0.246775i	$0.920629\pi$
$74$	−6.37267	−	8.59926i	−0.740808	−	0.999644i
$75$		0			0
$76$	−0.735776	+	2.41903i	−0.0843993	+	0.277481i
$77$		−	18.4911i		−	2.10726i
$78$	3.01667	−	2.89155i	0.341571	−	0.327404i
$79$			0.992853i			0.111705i	0.998439	+	0.0558524i	$0.0177876\pi$
$79$			0.992853i			0.111705i	−0.998439	+	0.0558524i	$0.982212\pi$
$80$		0			0
$81$	7.87288	−	4.36094i	0.874764	−	0.484549i
$82$	1.70594	−	1.26422i	0.188389	−	0.139610i
$83$	−7.72544			−0.847977			−0.423989	−	0.905668i	$-0.639370\pi$
$83$	−7.72544			−0.847977			−0.423989	+	0.905668i	$0.639370\pi$
$84$	−12.4447	−	2.12095i	−1.35782	−	0.231415i
$85$		0			0
$86$	−3.90455	+	2.89356i	−0.421039	+	0.312020i
$87$	0.232385	+	1.82779i	0.0249143	+	0.195959i
$88$	−4.81975	−	13.5180i	−0.513787	−	1.44102i
$89$		−	11.5742i		−	1.22687i	−0.789747	−	0.613433i	$-0.789788\pi$
$89$		−	11.5742i		−	1.22687i	0.789747	−	0.613433i	$-0.210212\pi$
$90$		0			0
$91$	6.21689			0.651708
$92$	−8.99447	−	2.73578i	−0.937738	−	0.285224i
$93$	−8.36687	+	1.06377i	−0.867604	+	0.110308i
$94$	12.4048	−	9.19282i	1.27945	−	0.948167i
$95$		0			0
$96$	−9.65055	+	1.69320i	−0.984955	+	0.172811i
$97$		−	7.40133i		−	0.751491i	−0.926723	−	0.375745i	$-0.877387\pi$
$97$		−	7.40133i		−	0.751491i	0.926723	−	0.375745i	$-0.122613\pi$
$98$	−5.28845	−	7.13622i	−0.534215	−	0.720867i
$99$	3.80911	+	14.7378i	0.382830	+	1.48120i
$100$		0			0
$101$	10.1535			1.01031			0.505157	−	0.863027i	$-0.331434\pi$
$101$	10.1535			1.01031			0.505157	+	0.863027i	$0.331434\pi$
$102$	7.21688	−	6.91756i	0.714577	−	0.684940i
$103$	15.5400			1.53120			0.765599	−	0.643318i	$-0.222443\pi$
$103$	15.5400			1.53120			0.765599	+	0.643318i	$0.222443\pi$
$104$	4.54489	−	1.62045i	0.445663	−	0.158898i
$105$		0			0
$106$	−10.0816	+	7.47116i	−0.979207	+	0.725663i
$107$	−14.8707			−1.43760			−0.718801	−	0.695216i	$-0.755309\pi$
$107$	−14.8707			−1.43760			−0.718801	+	0.695216i	$0.755309\pi$
$108$	10.3556	−	0.873117i	0.996464	−	0.0840157i
$109$			10.5376i			1.00932i	0.863319	+	0.504659i	$0.168382\pi$
$109$			10.5376i			1.00932i	−0.863319	+	0.504659i	$0.831618\pi$
$110$		0			0
$111$	1.65333	+	13.0040i	0.156927	+	1.23428i
$112$	−12.1083	−	8.11667i	−1.14412	−	0.766953i
$113$	−9.94353			−0.935409			−0.467704	−	0.883885i	$-0.654919\pi$
$113$	−9.94353			−0.935409			−0.467704	+	0.883885i	$0.654919\pi$
$114$	2.23557	−	2.14285i	0.209380	−	0.200696i
$115$		0			0
$116$	−0.619110	+	2.03546i	−0.0574830	+	0.188988i
$117$	−4.95499	+	1.28066i	−0.458089	+	0.118397i
$118$	−0.895716	+	0.663790i	−0.0824573	+	0.0611068i
$119$	14.8729			1.36339
$120$		0			0
$121$	−14.7458			−1.34052
$122$	0.713086	−	0.528448i	0.0645598	−	0.0478435i
$123$	−2.57976	+	0.327992i	−0.232609	+	0.0295740i
$124$	−9.31753	−	2.83404i	−0.836739	−	0.254504i
$125$		0			0
$126$	12.0212	+	9.72328i	1.07094	+	0.866219i
$127$	−5.62997			−0.499579			−0.249790	−	0.968300i	$-0.580361\pi$
$127$	−5.62997			−0.499579			−0.249790	+	0.968300i	$0.580361\pi$
$128$	−10.9674	−	2.77767i	−0.969393	−	0.245514i
$129$	5.90455	−	0.750707i	0.519867	−	0.0660961i
$130$		0			0
$131$		−	1.66215i		−	0.145223i	−0.997360	−	0.0726113i	$-0.976867\pi$
$131$		−	1.66215i		−	0.145223i	0.997360	−	0.0726113i	$-0.0231333\pi$
$132$	−2.95307	+	17.3271i	−0.257032	+	1.50813i
$133$	4.60717			0.399492
$134$	4.75143	−	3.52115i	0.410461	−	0.304181i
$135$		0			0
$136$	10.8729	−	3.87665i	0.932342	−	0.332420i
$137$	13.3554			1.14103			0.570515	−	0.821287i	$-0.306744\pi$
$137$	13.3554			1.14103			0.570515	+	0.821287i	$0.306744\pi$
$138$	7.96758	+	8.31234i	0.678246	+	0.707593i
$139$	−14.3540			−1.21749			−0.608745	−	0.793366i	$-0.708327\pi$
$139$	−14.3540			−1.21749			−0.608745	+	0.793366i	$0.708327\pi$
$140$		0			0
$141$	−18.7588	+	2.38500i	−1.57977	+	0.200853i
$142$	5.23476	+	7.06377i	0.439291	+	0.592778i
$143$		−	8.65598i		−	0.723850i
$144$	11.3226	+	3.97488i	0.943546	+	0.331240i
$145$		0			0
$146$	4.79132	−	3.55072i	0.396533	−	0.293859i
$147$	1.37204	+	10.7916i	0.113164	+	0.890072i
$148$	−4.40473	+	14.4815i	−0.362067	+	1.19037i
$149$	−18.2742			−1.49708			−0.748540	−	0.663089i	$-0.769245\pi$
$149$	−18.2742			−1.49708			−0.748540	+	0.663089i	$0.769245\pi$
$150$		0			0
$151$		−	16.7652i		−	1.36433i	−0.731197	−	0.682166i	$-0.761038\pi$
$151$		−	16.7652i		−	1.36433i	0.731197	−	0.682166i	$-0.238962\pi$
$152$	3.36809	−	1.20087i	0.273188	−	0.0974033i
$153$	−11.8540	+	3.06377i	−0.958339	+	0.247691i
$154$	−21.0100	+	15.5699i	−1.69303	+	1.25466i
$155$		0			0
$156$	−5.82555	−	0.992853i	−0.466417	−	0.0794919i
$157$	6.31311			0.503841			0.251920	−	0.967748i	$-0.418938\pi$
$157$	6.31311			0.503841			0.251920	+	0.967748i	$0.418938\pi$
$158$	1.12810	−	0.836004i	0.0897469	−	0.0665089i
$159$	15.2455	−	1.93832i	1.20905	−	0.153719i
$160$		0			0
$161$			17.1305i			1.35007i
$162$	−11.5841	−	5.27332i	−0.910135	−	0.414311i
$163$		−	2.69110i		−	0.210783i	−0.994431	−	0.105391i	$-0.966390\pi$
$163$		−	2.69110i		−	0.210783i	0.994431	−	0.105391i	$-0.0336096\pi$
$164$	−2.87288	−	0.873820i	−0.224334	−	0.0682339i
$165$		0			0
$166$	6.50499	+	8.77781i	0.504885	+	0.681290i
$167$			16.6633i			1.28945i	0.764416	+	0.644723i	$0.223027\pi$
$167$			16.6633i			1.28945i	−0.764416	+	0.644723i	$0.776973\pi$
$168$	8.06880	+	15.9258i	0.622522	+	1.22870i
$169$	−10.0898			−0.776136
$170$		0			0
$171$	−3.67201	+	0.949062i	−0.280805	+	0.0725766i
$172$	6.57544	+	2.00000i	0.501373	+	0.152499i
$173$			11.7458i			0.893013i	0.894780	+	0.446507i	$0.147332\pi$
$173$			11.7458i			0.893013i	−0.894780	+	0.446507i	$0.852668\pi$
$174$	1.88110	−	1.80308i	0.142605	−	0.136691i
$175$		0			0
$176$	−11.3011	+	16.8587i	−0.851852	+	1.27078i
$177$	1.35452	−	0.172214i	0.101812	−	0.0129444i
$178$	−13.1509	+	9.74575i	−0.985700	+	0.730475i
$179$			0.466861i			0.0348948i	0.999848	+	0.0174474i	$0.00555396\pi$
$179$			0.466861i			0.0348948i	−0.999848	+	0.0174474i	$0.994446\pi$
$180$		0			0
$181$		−	16.5628i		−	1.23110i	−0.788098	−	0.615550i	$-0.788934\pi$
$181$		−	16.5628i		−	1.23110i	0.788098	−	0.615550i	$-0.211066\pi$
$182$	−5.23476	−	7.06377i	−0.388026	−	0.523601i
$183$	−1.07834	+	0.137101i	−0.0797135	+	0.0101348i
$184$	4.46509	+	12.5233i	0.329171	+	0.923229i
$185$		0			0
$186$	8.25377	+	8.61090i	0.605196	+	0.631382i
$187$		−	20.7080i		−	1.51432i
$188$	−20.8902	−	6.35399i	−1.52357	−	0.463413i
$189$	−7.01300	−	17.5896i	−0.510121	−	1.27946i
$190$		0			0
$191$	−6.49110			−0.469679			−0.234840	−	0.972034i	$-0.575456\pi$
$191$	−6.49110			−0.469679			−0.234840	+	0.972034i	$0.575456\pi$
$192$	10.0498	+	9.53945i	0.725283	+	0.688451i
$193$		−	11.4013i		−	0.820685i	−0.911931	−	0.410343i	$-0.865409\pi$
$193$		−	11.4013i		−	0.820685i	0.911931	−	0.410343i	$-0.134591\pi$
$194$	−8.40954	+	6.23208i	−0.603770	+	0.447437i
$195$		0			0
$196$	−3.65533	+	12.0177i	−0.261095	+	0.858408i
$197$		−	3.56091i		−	0.253704i	−0.991922	−	0.126852i	$-0.959513\pi$
$197$		−	3.56091i		−	0.253704i	0.991922	−	0.126852i	$-0.0404874\pi$
$198$	13.5380	−	16.7375i	0.962106	−	1.18948i
$199$			4.40473i			0.312243i	0.987738	+	0.156122i	$0.0498992\pi$
$199$			4.40473i			0.312243i	−0.987738	+	0.156122i	$0.950101\pi$
$200$		0			0
$201$	−7.18522	+	0.913531i	−0.506806	+	0.0644355i
$202$	−8.54950	−	11.5367i	−0.601541	−	0.811717i
$203$	3.87665			0.272087
$204$	−13.9366	−	2.37523i	−0.975760	−	0.166300i
$205$		0			0
$206$	−13.0850	−	17.6568i	−0.911674	−	1.23021i
$207$	−3.52882	−	13.6533i	−0.245270	−	0.948972i
$208$	−5.66808	−	3.79954i	−0.393011	−	0.263451i
$209$		−	6.41471i		−	0.443715i
$210$		0			0
$211$	−16.1371			−1.11092			−0.555462	−	0.831542i	$-0.687459\pi$
$211$	−16.1371			−1.11092			−0.555462	+	0.831542i	$0.687459\pi$
$212$	16.9778	+	5.16400i	1.16604	+	0.354665i
$213$	−1.35811	−	10.6820i	−0.0930563	−	0.731918i
$214$	12.5214	+	16.8964i	0.855947	+	1.15501i
$215$		0			0
$216$	−9.71166	−	11.0310i	−0.660795	−	0.750566i
$217$			17.7458i			1.20466i
$218$	11.9730	−	8.87288i	0.810916	−	0.600947i
$219$	−7.24555	+	0.921202i	−0.489609	+	0.0622490i
$220$		0			0
$221$	6.96224			0.468331
$222$	13.3833	−	12.8282i	0.898226	−	0.860972i
$223$	−6.09474			−0.408134			−0.204067	−	0.978957i	$-0.565416\pi$
$223$	−6.09474			−0.408134			−0.204067	+	0.978957i	$0.565416\pi$
$224$	0.973105	+	20.5921i	0.0650183	+	1.37587i
$225$		0			0
$226$	8.37267	+	11.2981i	0.556942	+	0.751535i
$227$	−20.4673			−1.35846			−0.679230	−	0.733925i	$-0.737686\pi$
$227$	−20.4673			−1.35846			−0.679230	+	0.733925i	$0.737686\pi$
$228$	−4.31715	−	0.735776i	−0.285910	−	0.0487279i
$229$		−	26.4728i		−	1.74937i	−0.484693	−	0.874684i	$-0.661069\pi$
$229$		−	26.4728i		−	1.74937i	0.484693	−	0.874684i	$-0.338931\pi$
$230$		0			0
$231$	31.7718	−	4.03947i	2.09043	−	0.265778i
$232$	2.83404	−	1.01046i	0.186064	−	0.0663398i
$233$	24.3773			1.59701			0.798504	−	0.601989i	$-0.205625\pi$
$233$	24.3773			1.59701			0.798504	+	0.601989i	$0.205625\pi$
$234$	5.62733	+	4.55163i	0.367870	+	0.297549i
$235$		0			0
$236$	1.50842	+	0.458805i	0.0981901	+	0.0298657i
$237$	−1.70594	+	0.216894i	−0.110813	+	0.0140888i
$238$	−12.5233	−	16.8989i	−0.811764	−	1.09539i
$239$	−5.47155			−0.353925			−0.176963	−	0.984218i	$-0.556627\pi$
$239$	−5.47155			−0.353925			−0.176963	+	0.984218i	$0.556627\pi$
$240$		0			0
$241$	24.6446			1.58750			0.793750	−	0.608244i	$-0.208126\pi$
$241$	24.6446			1.58750			0.793750	+	0.608244i	$0.208126\pi$
$242$	12.4162	+	16.7544i	0.798147	+	1.07702i
$243$	9.21292	+	12.5747i	0.591009	+	0.806665i
$244$	−1.20087	−	0.365259i	−0.0768777	−	0.0233833i
$245$		0			0
$246$	2.54489	+	2.65500i	0.162256	+	0.169277i
$247$	2.15669			0.137227
$248$	4.62547	+	12.9731i	0.293718	+	0.823793i
$249$	−1.68766	−	13.2740i	−0.106951	−	0.841205i
$250$		0			0
$251$			1.74973i			0.110442i	0.998474	+	0.0552210i	$0.0175863\pi$
$251$			1.74973i			0.110442i	−0.998474	+	0.0552210i	$0.982414\pi$
$252$	0.925666	−	21.8460i	0.0583115	−	1.37617i
$253$	23.8513			1.49952
$254$	4.74056	+	6.39689i	0.297449	+	0.401377i
$255$		0			0
$256$	6.07877	+	14.8003i	0.379923	+	0.925018i
$257$	5.27646			0.329137			0.164568	−	0.986366i	$-0.447377\pi$
$257$	5.27646			0.329137			0.164568	+	0.986366i	$0.447377\pi$
$258$	−5.82473	−	6.07677i	−0.362632	−	0.378323i
$259$	27.5809			1.71379
$260$		0			0
$261$	−3.08977	+	0.798578i	−0.191252	+	0.0494307i
$262$	−1.88857	+	1.39957i	−0.116676	+	0.0864655i
$263$		−	1.79043i		−	0.110403i	−0.998475	−	0.0552014i	$-0.982420\pi$
$263$		−	1.79043i		−	0.110403i	0.998475	−	0.0552014i	$-0.0175801\pi$
$264$	22.1740	−	11.2345i	1.36471	−	0.691433i
$265$		0			0
$266$	−3.87934	−	5.23476i	−0.237857	−	0.320964i
$267$	19.8871	−	2.52845i	1.21707	−	0.154739i
$268$	−8.00161	−	2.43379i	−0.488776	−	0.148667i
$269$	18.7080			1.14065			0.570323	−	0.821420i	$-0.306818\pi$
$269$	18.7080			1.14065			0.570323	+	0.821420i	$0.306818\pi$
$270$		0			0
$271$		−	24.8441i		−	1.50917i	−0.656200	−	0.754587i	$-0.727837\pi$
$271$		−	24.8441i		−	1.50917i	0.656200	−	0.754587i	$-0.272163\pi$
$272$	−13.5599	−	9.08977i	−0.822192	−	0.551148i
$273$	1.35811	+	10.6820i	0.0821967	+	0.646503i
$274$	−11.2455	−	15.1747i	−0.679368	−	0.916737i
$275$		0			0
$276$	2.73578	−	16.0521i	0.164674	−	0.966224i
$277$	−29.2030			−1.75464			−0.877319	−	0.479908i	$-0.840670\pi$
$277$	−29.2030			−1.75464			−0.877319	+	0.479908i	$0.840670\pi$
$278$	12.0864	+	16.3093i	0.724893	+	0.978168i
$279$	−3.65557	−	14.1437i	−0.218853	−	0.846763i
$280$		0			0
$281$		−	22.9856i		−	1.37121i	−0.727975	−	0.685604i	$-0.759538\pi$
$281$		−	22.9856i		−	1.37121i	0.727975	−	0.685604i	$-0.240462\pi$
$282$	18.5052	+	19.3059i	1.10197	+	1.14965i
$283$			2.03511i			0.120975i	0.998169	+	0.0604875i	$0.0192655\pi$
$283$			2.03511i			0.120975i	−0.998169	+	0.0604875i	$0.980734\pi$
$284$	3.61822	−	11.8957i	0.214702	−	0.705880i
$285$		0			0
$286$	−9.83511	+	7.28853i	−0.581562	+	0.430980i
$287$			5.47155i			0.322975i
$288$	−5.01749	−	16.2119i	−0.295659	−	0.955294i
$289$	−0.344017			−0.0202363
$290$		0			0
$291$	12.7171	−	1.61686i	0.745490	−	0.0947818i
$292$	−8.06880	−	2.45422i	−0.472191	−	0.143623i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	11.1063	−	10.6457i	0.647733	−	0.620868i
$295$		0			0
$296$	20.1631	−	7.18902i	1.17196	−	0.417853i
$297$	−24.4906	+	9.76443i	−1.42109	+	0.566590i
$298$	15.3873	+	20.7635i	0.891361	+	1.20280i
$299$			8.01905i			0.463753i
$300$		0			0
$301$		−	12.5233i		−	0.721830i
$302$	−19.0490	+	14.1167i	−1.09615	+	0.812323i
$303$	2.21809	+	17.4460i	0.127426	+	1.00225i
$304$	−4.20046	−	2.81574i	−0.240913	−	0.161494i
$305$		0			0
$306$	13.4624	+	10.8890i	0.769597	+	0.622483i
$307$			19.0547i			1.08751i	0.839245	+	0.543753i	$0.182997\pi$
$307$			19.0547i			1.08751i	−0.839245	+	0.543753i	$0.817003\pi$
$308$	35.3817	+	10.7618i	2.01606	+	0.613209i
$309$	3.39478	+	26.7011i	0.193122	+	1.51897i
$310$		0			0
$311$	−26.0902			−1.47944			−0.739719	−	0.672916i	$-0.765042\pi$
$311$	−26.0902			−1.47944			−0.739719	+	0.672916i	$0.765042\pi$
$312$	3.77714	+	7.45511i	0.213838	+	0.422063i
$313$		−	20.1795i		−	1.14062i	−0.821431	−	0.570308i	$-0.806824\pi$
$313$		−	20.1795i		−	1.14062i	0.821431	−	0.570308i	$-0.193176\pi$
$314$	−5.31577	−	7.17309i	−0.299987	−	0.404801i
$315$		0			0
$316$	−1.89977	−	0.577838i	−0.106871	−	0.0325060i
$317$		−	7.81598i		−	0.438989i	−0.975614	−	0.219495i	$-0.929559\pi$
$317$		−	7.81598i		−	0.438989i	0.975614	−	0.219495i	$-0.0704408\pi$
$318$	−15.0395	−	15.6902i	−0.843371	−	0.879863i
$319$		−	5.39759i		−	0.302207i
$320$		0			0
$321$	−3.24857	−	25.5511i	−0.181318	−	1.42612i
$322$	19.4640	−	14.4242i	1.08469	−	0.803830i
$323$	5.15952			0.287083
$324$	3.76243	+	17.6024i	0.209024	+	0.977911i
$325$		0			0
$326$	−3.05768	+	2.26596i	−0.169349	+	0.125500i
$327$	−18.1059	+	2.30199i	−1.00126	+	0.127300i
$328$	1.42617	+	4.00000i	0.0787472	+	0.220863i
$329$			39.7865i			2.19350i
$330$		0			0
$331$	−10.0424			−0.551982			−0.275991	−	0.961160i	$-0.589006\pi$
$331$	−10.0424			−0.551982			−0.275991	+	0.961160i	$0.589006\pi$
$332$	4.49619	−	14.7822i	0.246760	−	0.811279i
$333$	−21.9825	+	5.68157i	−1.20464	+	0.311348i
$334$	18.9332	−	14.0309i	1.03598	−	0.767735i
$335$		0			0
$336$	11.3011	−	22.5778i	0.616525	−	1.23172i
$337$		−	17.8733i		−	0.973620i	−0.873508	−	0.486810i	$-0.838160\pi$
$337$		−	17.8733i		−	0.973620i	0.873508	−	0.486810i	$-0.161840\pi$
$338$	8.49581	+	11.4642i	0.462111	+	0.623571i
$339$	−2.17221	−	17.0852i	−0.117978	−	0.927939i
$340$		0			0
$341$	24.7080			1.33801
$342$	4.17026	+	3.37308i	0.225502	+	0.182395i
$343$	−2.62146			−0.141546
$344$	−3.26422	−	9.15520i	−0.175995	−	0.493615i
$345$		0			0
$346$	13.3458	−	9.89018i	0.717473	−	0.531700i
$347$	34.9886			1.87829			0.939143	−	0.343525i	$-0.111621\pi$
$347$	34.9886			1.87829			0.939143	+	0.343525i	$0.111621\pi$
$348$	−3.63262	−	0.619110i	−0.194729	−	0.0331878i
$349$			8.24993i			0.441609i	0.975318	+	0.220804i	$0.0708682\pi$
$349$			8.24993i			0.441609i	−0.975318	+	0.220804i	$0.929132\pi$
$350$		0			0
$351$	−3.28290	−	8.23400i	−0.175228	−	0.439498i
$352$	28.6710	−	1.35489i	1.52817	−	0.0722157i
$353$	−0.935042			−0.0497673			−0.0248836	−	0.999690i	$-0.507922\pi$
$353$	−0.935042			−0.0497673			−0.0248836	+	0.999690i	$0.507922\pi$
$354$	−1.33621	−	1.39403i	−0.0710188	−	0.0740917i
$355$		0			0
$356$	22.1467	+	6.73618i	1.17377	+	0.357017i
$357$	3.24906	+	25.5549i	0.171958	+	1.35251i
$358$	0.530457	−	0.393107i	0.0280355	−	0.0207763i
$359$	−32.5813			−1.71957			−0.859787	−	0.510653i	$-0.829404\pi$
$359$	−32.5813			−1.71957			−0.859787	+	0.510653i	$0.829404\pi$
$360$		0			0
$361$	−17.4017			−0.915881
$362$	−18.8190	+	13.9462i	−0.989103	+	0.732997i
$363$	−3.22128	−	25.3364i	−0.169074	−	1.32982i
$364$	−3.61822	+	11.8957i	−0.189646	+	0.623504i
$365$		0			0
$366$	1.06377	+	1.10980i	0.0556040	+	0.0580100i
$367$	0.791919			0.0413378			0.0206689	−	0.999786i	$-0.493420\pi$
$367$	0.791919			0.0413378			0.0206689	+	0.999786i	$0.493420\pi$
$368$	10.4695	−	15.6182i	0.545762	−	0.814156i
$369$	−1.12712	−	4.36094i	−0.0586757	−	0.227022i
$370$		0			0
$371$		−	32.3351i		−	1.67876i
$372$	2.83404	−	16.6287i	0.146938	−	0.862157i
$373$	−18.7335			−0.969982			−0.484991	−	0.874519i	$-0.661177\pi$
$373$	−18.7335			−0.969982			−0.484991	+	0.874519i	$0.661177\pi$
$374$	−23.5289	+	17.4366i	−1.21665	+	0.901624i
$375$		0			0
$376$	10.3704	+	29.0861i	0.534814	+	1.50000i
$377$	1.81472			0.0934630
$378$	−14.0806	+	22.7792i	−0.724229	+	1.17164i
$379$	−8.88244			−0.456260			−0.228130	−	0.973631i	$-0.573261\pi$
$379$	−8.88244			−0.456260			−0.228130	+	0.973631i	$0.573261\pi$
$380$		0			0
$381$	−1.22990	−	9.67352i	−0.0630095	−	0.495590i
$382$	5.46565	+	7.37532i	0.279647	+	0.377354i
$383$			3.48418i			0.178033i	0.996030	+	0.0890167i	$0.0283724\pi$
$383$			3.48418i			0.178033i	−0.996030	+	0.0890167i	$0.971628\pi$
$384$	2.37676	−	19.4512i	0.121288	−	0.992617i
$385$		0			0
$386$	−12.9544	+	9.60017i	−0.659363	+	0.488636i
$387$	2.57976	+	9.98132i	0.131137	+	0.507379i
$388$	14.1620	+	4.30756i	0.718969	+	0.218683i
$389$	24.8027			1.25754			0.628772	−	0.777590i	$-0.283558\pi$
$389$	24.8027			1.25754			0.628772	+	0.777590i	$0.283558\pi$
$390$		0			0
$391$			19.1842i			0.970188i
$392$	16.7326	−	5.96591i	0.845126	−	0.301324i
$393$	2.85594	−	0.363105i	0.144063	−	0.0183162i
$394$	−4.04598	+	2.99837i	−0.203834	+	0.151055i
$395$		0			0
$396$	−30.4169	−	1.28883i	−1.52851	−	0.0647664i
$397$	−15.5873			−0.782306			−0.391153	−	0.920326i	$-0.627924\pi$
$397$	−15.5873			−0.782306			−0.391153	+	0.920326i	$0.627924\pi$
$398$	5.00475	−	3.70888i	0.250865	−	0.185909i
$399$	1.00646	+	7.91612i	0.0503860	+	0.396302i
$400$		0			0
$401$			26.3852i			1.31761i	0.752313	+	0.658806i	$0.228938\pi$
$401$			26.3852i			1.31761i	−0.752313	+	0.658806i	$0.771062\pi$
$402$	7.08808	+	7.39478i	0.353521	+	0.368818i
$403$			8.30708i			0.413805i
$404$	−5.90934	+	19.4283i	−0.294001	+	0.966592i
$405$		0			0
$406$	−3.26422	−	4.40473i	−0.162001	−	0.218603i
$407$		−	38.4017i		−	1.90350i
$408$	9.03617	+	17.8351i	0.447357	+	0.882970i
$409$	0.497143			0.0245821			0.0122911	−	0.999924i	$-0.496088\pi$
$409$	0.497143			0.0245821			0.0122911	+	0.999924i	$0.496088\pi$
$410$		0			0
$411$	2.91756	+	22.9475i	0.143912	+	1.13192i
$412$	−9.04422	+	29.7349i	−0.445577	+	1.46493i
$413$		−	2.87288i		−	0.141365i
$414$	−12.5419	+	15.5059i	−0.616399	+	0.762075i
$415$		0			0
$416$	0.455526	+	9.63949i	0.0223340	+	0.472615i
$417$	−3.13570	−	24.6633i	−0.153556	−	1.20777i
$418$	−7.28853	+	5.40133i	−0.356494	+	0.264187i
$419$		−	11.0240i		−	0.538556i	−0.963063	−	0.269278i	$-0.913215\pi$
$419$		−	11.0240i		−	0.538556i	0.963063	−	0.269278i	$-0.0867850\pi$
$420$		0			0
$421$			11.0971i			0.540840i	0.962742	+	0.270420i	$0.0871626\pi$
$421$			11.0971i			0.540840i	−0.962742	+	0.270420i	$0.912837\pi$
$422$	13.5878	+	18.3353i	0.661443	+	0.892549i
$423$	−8.19589	−	31.7106i	−0.398498	−	1.54182i
$424$	−8.42822	−	23.6387i	−0.409311	−	1.14800i
$425$		0			0
$426$	−10.9935	+	10.5376i	−0.532639	+	0.510548i
$427$			2.28712i			0.110681i
$428$	8.65470	−	28.4542i	0.418340	−	1.37539i
$429$	14.8729	−	1.89094i	0.718069	−	0.0912956i
$430$		0			0
$431$	6.84000			0.329471			0.164736	−	0.986338i	$-0.447323\pi$
$431$	6.84000			0.329471			0.164736	+	0.986338i	$0.447323\pi$
$432$	−4.35625	+	20.3230i	−0.209590	+	0.977789i
$433$			38.6378i			1.85681i	0.371567	+	0.928406i	$0.378821\pi$
$433$			38.6378i			1.85681i	−0.371567	+	0.928406i	$0.621179\pi$
$434$	20.1631	−	14.9423i	0.967860	−	0.717254i
$435$		0			0
$436$	−20.1631	−	6.13285i	−0.965638	−	0.293710i
$437$			5.94269i			0.284277i
$438$	7.14760	+	7.45687i	0.341526	+	0.356303i
$439$			4.07908i			0.194684i	0.995251	+	0.0973420i	$0.0310341\pi$
$439$			4.07908i			0.194684i	−0.995251	+	0.0973420i	$0.968966\pi$
$440$		0			0
$441$	−18.2425	+	4.71494i	−0.868692	+	0.224521i
$442$	−5.86236	−	7.91064i	−0.278844	−	0.376271i
$443$	12.7140			0.604059			0.302030	−	0.953299i	$-0.402336\pi$
$443$	12.7140			0.604059			0.302030	+	0.953299i	$0.402336\pi$
$444$	−25.8447	−	4.40473i	−1.22653	−	0.209039i
$445$		0			0
$446$	5.13191	+	6.92498i	0.243003	+	0.327907i
$447$	−3.99209	−	31.3991i	−0.188819	−	1.48513i
$448$	22.5778	−	18.4447i	1.06670	−	0.871428i
$449$			31.2985i			1.47707i	0.674217	+	0.738533i	$0.264481\pi$
$449$			31.2985i			1.47707i	−0.674217	+	0.738533i	$0.735519\pi$
$450$		0			0
$451$	7.61822			0.358728
$452$	5.78711	−	19.0264i	0.272203	−	0.894927i
$453$	28.8063	−	3.66244i	1.35344	−	0.172077i
$454$	17.2339	+	23.2554i	0.808827	+	1.09143i
$455$		0			0
$456$	2.79913	+	5.52478i	0.131081	+	0.258721i
$457$			29.1097i			1.36170i	0.732425	+	0.680848i	$0.238388\pi$
$457$			29.1097i			1.36170i	−0.732425	+	0.680848i	$0.761612\pi$
$458$	−30.0789	+	22.2906i	−1.40549	+	1.04157i
$459$	−7.85379	−	19.6985i	−0.366583	−	0.919446i
$460$		0			0
$461$	0.00687071			0.000320001			0.000160001	−	1.00000i	$-0.499949\pi$
$461$	0.00687071			0.000320001			0.000160001		1.00000i	$0.499949\pi$
$462$	−31.3423	−	32.6984i	−1.45817	−	1.52127i
$463$	17.9904			0.836086			0.418043	−	0.908427i	$-0.362716\pi$
$463$	17.9904			0.836086			0.418043	+	0.908427i	$0.362716\pi$
$464$	−3.53443	−	2.36927i	−0.164082	−	0.109991i
$465$		0			0
$466$	−20.5262	−	27.6980i	−0.950858	−	1.28308i
$467$	−3.99927			−0.185064			−0.0925321	−	0.995710i	$-0.529496\pi$
$467$	−3.99927			−0.185064			−0.0925321	+	0.995710i	$0.529496\pi$
$468$	0.433319	−	10.2265i	0.0200302	−	0.472718i
$469$			15.2395i			0.703695i
$470$		0			0
$471$	1.37913	+	10.8473i	0.0635470	+	0.499817i
$472$	−0.748822	−	2.10023i	−0.0344673	−	0.0966708i
$473$	−17.4366			−0.801735
$474$	1.68288	+	1.75570i	0.0772971	+	0.0806418i
$475$		0			0
$476$	−8.65598	+	28.4585i	−0.396746	+	1.30439i
$477$	6.66093	+	25.7718i	0.304983	+	1.18001i
$478$	4.60717	+	6.21689i	0.210727	+	0.284354i
$479$	−34.1467			−1.56020			−0.780101	−	0.625654i	$-0.784832\pi$
$479$	−34.1467			−1.56020			−0.780101	+	0.625654i	$0.784832\pi$
$480$		0			0
$481$	12.9111			0.588693
$482$	−20.7513	−	28.0018i	−0.945197	−	1.27545i
$483$	−29.4339	+	3.74223i	−1.33929	+	0.170278i
$484$	8.58200	−	28.2152i	0.390091	−	1.28251i
$485$		0			0
$486$	6.53011	−	21.0561i	0.296212	−	0.955122i
$487$	0.851820			0.0385997			0.0192998	−	0.999814i	$-0.493856\pi$
$487$	0.851820			0.0385997			0.0192998	+	0.999814i	$0.493856\pi$
$488$	0.596143	+	1.67201i	0.0269861	+	0.0756883i
$489$	4.62389	−	0.587884i	0.209100	−	0.0265850i
$490$		0			0
$491$			6.09115i			0.274890i	0.990509	+	0.137445i	$0.0438890\pi$
$491$			6.09115i			0.274890i	−0.990509	+	0.137445i	$0.956111\pi$
$492$	0.873820	−	5.12712i	0.0393949	−	0.231149i
$493$	4.34142			0.195528
$494$	−1.81598	−	2.45048i	−0.0817048	−	0.110252i
$495$		0			0
$496$	10.8456	−	16.1792i	0.486980	−	0.726468i
$497$	−22.6560			−1.01626
$498$	−13.6612	+	13.0946i	−0.612171	+	0.586781i
$499$	−13.1375			−0.588116			−0.294058	−	0.955788i	$-0.595006\pi$
$499$	−13.1375			−0.588116			−0.294058	+	0.955788i	$0.595006\pi$
$500$		0			0
$501$	−28.6312	+	3.64018i	−1.27915	+	0.162631i
$502$	1.98808	−	1.47331i	0.0887324	−	0.0657571i
$503$			27.6064i			1.23091i	0.788172	+	0.615455i	$0.211028\pi$
$503$			27.6064i			1.23091i	−0.788172	+	0.615455i	$0.788972\pi$
$504$	−25.6013	+	17.3430i	−1.14037	+	0.772520i
$505$		0			0
$506$	−20.0833	−	27.1003i	−0.892812	−	1.20476i
$507$	−2.20416	−	17.3364i	−0.0978902	−	0.769938i
$508$	3.27663	−	10.7726i	0.145377	−	0.477959i
$509$	5.46468			0.242218			0.121109	−	0.992639i	$-0.461355\pi$
$509$	5.46468			0.242218			0.121109	+	0.992639i	$0.461355\pi$
$510$		0			0
$511$			15.3675i			0.679817i
$512$	11.6979	−	19.3690i	0.516981	−	0.855997i
$513$	−2.43287	−	6.10199i	−0.107414	−	0.269409i
$514$	−4.44290	−	5.99523i	−0.195968	−	0.264438i
$515$		0			0
$516$	−2.00000	+	11.7350i	−0.0880451	+	0.516603i
$517$	55.3960			2.43631
$518$	−23.2237	−	31.3380i	−1.02039	−	1.37691i
$519$	−20.1818	+	2.56592i	−0.885882	+	0.112631i
$520$		0			0
$521$			39.1312i			1.71437i	0.515010	+	0.857184i	$0.327788\pi$
$521$			39.1312i			1.71437i	−0.515010	+	0.857184i	$0.672212\pi$
$522$	3.50902	+	2.83824i	0.153585	+	0.124227i
$523$			14.3467i			0.627336i	0.949533	+	0.313668i	$0.101558\pi$
$523$			14.3467i			0.627336i	−0.949533	+	0.313668i	$0.898442\pi$
$524$	3.18043	+	0.967367i	0.138938	+	0.0422596i
$525$		0			0
$526$	−2.03433	+	1.50758i	−0.0887009	+	0.0657338i
$527$			19.8733i			0.865694i
$528$	−31.4358	−	15.7349i	−1.36807	−	0.684773i
$529$	0.903770			0.0392944
$530$		0			0
$531$	0.591804	+	2.28974i	0.0256821	+	0.0993664i
$532$	−2.68136	+	8.81557i	−0.116252	+	0.382203i
$533$			2.56132i			0.110943i
$534$	−19.6182	−	20.4671i	−0.848963	−	0.885698i
$535$		0			0
$536$	3.97221	+	11.1409i	0.171574	+	0.481214i
$537$	−0.802169	+	0.101988i	−0.0346161	+	0.00440111i
$538$	−15.7525	−	21.2564i	−0.679140	−	0.916429i
$539$		−	31.8682i		−	1.37266i
$540$		0			0
$541$			29.8846i			1.28484i	0.766352	+	0.642420i	$0.222070\pi$
$541$			29.8846i			1.28484i	−0.766352	+	0.642420i	$0.777930\pi$
$542$	−28.2284	+	20.9193i	−1.21252	+	0.898562i
$543$	28.4585	−	3.61822i	1.22127	−	0.155273i
$544$	1.08977	+	23.0609i	0.0467235	+	0.988727i
$545$		0			0
$546$	10.9935	−	10.5376i	0.470480	−	0.450967i
$547$		−	2.78046i		−	0.118884i	−0.998232	−	0.0594418i	$-0.981068\pi$
$547$		−	2.78046i		−	0.118884i	0.998232	−	0.0594418i	$-0.0189321\pi$
$548$	−7.77282	+	25.5549i	−0.332038	+	1.09165i
$549$	−0.471140	−	1.82288i	−0.0201078	−	0.0777987i
$550$		0			0
$551$	1.34484			0.0572921
$552$	−20.5423	+	10.4078i	−0.874340	+	0.442985i
$553$			3.61822i			0.153862i
$554$	24.5896	+	33.1811i	1.04471	+	1.40973i
$555$		0			0
$556$	8.35399	−	27.4656i	0.354288	−	1.16480i
$557$			39.3640i			1.66791i	0.551836	+	0.833953i	$0.313927\pi$
$557$			39.3640i			1.66791i	−0.551836	+	0.833953i	$0.686073\pi$
$558$	−12.9923	+	16.0629i	−0.550010	+	0.679996i
$559$		−	5.86236i		−	0.247951i
$560$		0			0
$561$	35.5809	−	4.52376i	1.50223	−	0.190994i
$562$	−26.1168	+	19.3544i	−1.10167	+	0.816416i
$563$	16.1259			0.679624			0.339812	−	0.940493i	$-0.389637\pi$
$563$	16.1259			0.679624			0.339812	+	0.940493i	$0.389637\pi$
$564$	6.35399	−	37.2819i	0.267551	−	1.56985i
$565$		0			0
$566$	2.31234	−	1.71361i	0.0971949	−	0.0720284i
$567$	28.6908	−	15.8924i	1.20490	−	0.667419i
$568$	−16.5628	+	5.90534i	−0.694958	+	0.247783i
$569$		−	8.55906i		−	0.358814i	−0.983775	−	0.179407i	$-0.942582\pi$
$569$		−	8.55906i		−	0.358814i	0.983775	−	0.179407i	$-0.0574180\pi$
$570$		0			0
$571$	34.6984			1.45208			0.726042	−	0.687650i	$-0.241358\pi$
$571$	34.6984			1.45208			0.726042	+	0.687650i	$0.241358\pi$
$572$	16.5628	+	5.03776i	0.692524	+	0.210639i
$573$	−1.41801	−	11.1531i	−0.0592383	−	0.465929i
$574$	6.21689	−	4.60717i	0.259488	−	0.192299i
$575$		0			0
$576$	−14.1954	+	19.3517i	−0.591476	+	0.806322i
$577$		−	32.8684i		−	1.36833i	−0.729328	−	0.684165i	$-0.760167\pi$
$577$		−	32.8684i		−	1.36833i	0.729328	−	0.684165i	$-0.239833\pi$
$578$	0.289670	+	0.390879i	0.0120487	+	0.0162584i
$579$	19.5900	−	2.49068i	0.814132	−	0.103509i
$580$		0			0
$581$	−28.1535			−1.16801
$582$	−12.5452	−	13.0880i	−0.520015	−	0.542516i
$583$	−45.0212			−1.86459
$584$	4.00557	+	11.2345i	0.165752	+	0.464885i
$585$		0			0
$586$	6.81733	−	5.05213i	0.281621	−	0.208702i
$587$	−15.4302			−0.636872			−0.318436	−	0.947944i	$-0.603158\pi$
$587$	−15.4302			−0.636872			−0.318436	+	0.947944i	$0.603158\pi$
$588$	−21.4476	−	3.65533i	−0.884484	−	0.150743i
$589$			6.15614i			0.253659i
$590$		0			0
$591$	6.11843	−	0.777899i	0.251678	−	0.0319985i
$592$	−25.1461	−	16.8564i	−1.03350	−	0.692795i
$593$	−14.0511			−0.577008			−0.288504	−	0.957479i	$-0.593158\pi$
$593$	−14.0511			−0.577008			−0.288504	+	0.957479i	$0.593158\pi$
$594$	31.7162	+	19.6049i	1.30133	+	0.804400i
$595$		0			0
$596$	10.6355	−	34.9667i	0.435649	−	1.43229i
$597$	−7.56830	+	0.962236i	−0.309750	+	0.0393817i
$598$	9.11141	−	6.75221i	0.372593	−	0.276119i
$599$	30.0200			1.22658			0.613291	−	0.789857i	$-0.289845\pi$
$599$	30.0200			1.22658			0.613291	+	0.789857i	$0.289845\pi$
$600$		0			0
$601$	−29.3006			−1.19520			−0.597599	−	0.801795i	$-0.703878\pi$
$601$	−29.3006			−1.19520			−0.597599	+	0.801795i	$0.703878\pi$
$602$	−14.2292	+	10.5449i	−0.579940	+	0.429777i
$603$	−3.13929	−	12.1462i	−0.127842	−	0.494632i
$604$	32.0793	+	9.75731i	1.30529	+	0.397019i
$605$		0			0
$606$	17.9548	−	17.2102i	0.729366	−	0.699115i
$607$	38.9265			1.57998			0.789989	−	0.613122i	$-0.210086\pi$
$607$	38.9265			1.57998			0.789989	+	0.613122i	$0.210086\pi$
$608$	0.337578	+	7.14356i	0.0136906	+	0.289710i
$609$	0.846874	+	6.66093i	0.0343171	+	0.269915i
$610$		0			0
$611$			18.6247i			0.753474i
$612$	1.03664	−	24.4651i	0.0419038	−	0.988943i
$613$	−28.9092			−1.16763			−0.583816	−	0.811886i	$-0.698441\pi$
$613$	−28.9092			−1.16763			−0.583816	+	0.811886i	$0.698441\pi$
$614$	21.6503	−	16.0444i	0.873735	−	0.647501i
$615$		0			0
$616$	−17.5644	−	49.2631i	−0.707691	−	1.98487i
$617$	−26.5340			−1.06822			−0.534109	−	0.845416i	$-0.679353\pi$
$617$	−26.5340			−1.06822			−0.534109	+	0.845416i	$0.679353\pi$
$618$	27.4798	−	26.3401i	1.10540	−	1.05955i
$619$	17.9531			0.721595			0.360798	−	0.932644i	$-0.382505\pi$
$619$	17.9531			0.721595			0.360798	+	0.932644i	$0.382505\pi$
$620$		0			0
$621$	22.6885	−	9.04593i	0.910459	−	0.363001i
$622$	21.9685	+	29.6442i	0.880857	+	1.18863i
$623$		−	42.1795i		−	1.68989i
$624$	5.29023	−	10.5690i	0.211779	−	0.423100i
$625$		0			0
$626$	−22.9284	+	16.9916i	−0.916404	+	0.679122i
$627$	11.0219	−	1.40133i	0.440171	−	0.0559635i
$628$	−3.67421	+	12.0798i	−0.146617	+	0.482036i
$629$	30.8875			1.23157
$630$		0			0
$631$			33.8875i			1.34904i	0.738257	+	0.674520i	$0.235649\pi$
$631$			33.8875i			1.34904i	−0.738257	+	0.674520i	$0.764351\pi$
$632$	0.943097	+	2.64511i	0.0375144	+	0.105217i
$633$	−3.52523	−	27.7271i	−0.140115	−	1.10205i
$634$	−8.88068	+	6.58123i	−0.352697	+	0.261374i
$635$		0			0
$636$	−5.16400	+	30.2996i	−0.204766	+	1.20146i
$637$	10.7144			0.424521
$638$	−6.13285	+	4.54489i	−0.242802	+	0.179934i
$639$	18.0573	−	4.66707i	0.714336	−	0.184626i
$640$		0			0
$641$		−	16.1456i		−	0.637711i	−0.947803	−	0.318856i	$-0.896702\pi$
$641$		−	16.1456i		−	0.637711i	0.947803	−	0.318856i	$-0.103298\pi$
$642$	−26.2963	+	25.2057i	−1.03783	+	0.994788i
$643$		−	41.9604i		−	1.65476i	−0.561645	−	0.827378i	$-0.689831\pi$
$643$		−	41.9604i		−	1.65476i	0.561645	−	0.827378i	$-0.310169\pi$
$644$	−32.7782	−	9.96989i	−1.29164	−	0.392869i
$645$		0			0
$646$	−4.34443	−	5.86236i	−0.170929	−	0.230651i
$647$		−	9.10158i		−	0.357820i	−0.983865	−	0.178910i	$-0.942743\pi$
$647$		−	9.10158i		−	0.357820i	0.983865	−	0.178910i	$-0.0572571\pi$
$648$	16.8322	−	19.0966i	0.661230	−	0.750183i
$649$	−4.00000			−0.157014
$650$		0			0
$651$	−30.4911	+	3.87665i	−1.19504	+	0.151938i
$652$	5.14927	+	1.56621i	0.201661	+	0.0613376i
$653$		−	12.0573i		−	0.471839i	−0.971773	−	0.235919i	$-0.924190\pi$
$653$		−	12.0573i		−	0.471839i	0.971773	−	0.235919i	$-0.0758102\pi$
$654$	17.8611	+	18.6340i	0.698425	+	0.728646i
$655$		0			0
$656$	3.34402	−	4.98854i	0.130562	−	0.194770i
$657$	−3.16565	−	12.2482i	−0.123504	−	0.477848i
$658$	45.2062	−	33.5011i	1.76232	−	1.30601i
$659$			12.1916i			0.474916i	0.971398	+	0.237458i	$0.0763142\pi$
$659$			12.1916i			0.474916i	−0.971398	+	0.237458i	$0.923686\pi$
$660$		0			0
$661$			22.0284i			0.856806i	0.903588	+	0.428403i	$0.140924\pi$
$661$			22.0284i			0.856806i	−0.903588	+	0.428403i	$0.859076\pi$
$662$	8.45596	+	11.4104i	0.328650	+	0.443479i
$663$	1.52094	+	11.9626i	0.0590682	+	0.464591i
$664$	−20.5818	+	7.33828i	−0.798727	+	0.284781i
$665$		0			0
$666$	24.9653	+	20.1930i	0.967386	+	0.782463i
$667$			5.00041i			0.193617i
$668$	−31.8844	−	9.69801i	−1.23364	−	0.375227i
$669$	−1.33143	−	10.4721i	−0.0514759	−	0.404875i
$670$		0			0
$671$	3.18443			0.122934
$672$	−35.1691	+	6.17045i	−1.35668	+	0.238030i
$673$		−	25.3258i		−	0.976238i	−0.872777	−	0.488119i	$-0.837683\pi$
$673$		−	25.3258i		−	0.976238i	0.872777	−	0.488119i	$-0.162317\pi$
$674$	−20.3080	+	15.0497i	−0.782235	+	0.579693i
$675$		0			0
$676$	5.87223	−	19.3062i	0.225855	−	0.742548i
$677$		−	21.9435i		−	0.843358i	−0.906745	−	0.421679i	$-0.861441\pi$
$677$		−	21.9435i		−	0.843358i	0.906745	−	0.421679i	$-0.138559\pi$
$678$	−17.5835	+	16.8542i	−0.675289	+	0.647282i
$679$		−	26.9724i		−	1.03511i
$680$		0			0
$681$	−4.47118	−	35.1673i	−0.171336	−	1.34761i
$682$	−20.8047	−	28.0737i	−0.796652	−	1.07500i
$683$	−16.0383			−0.613687			−0.306844	−	0.951760i	$-0.599273\pi$
$683$	−16.0383			−0.613687			−0.306844	+	0.951760i	$0.599273\pi$
$684$	0.321121	−	7.57854i	0.0122784	−	0.289773i
$685$		0			0
$686$	2.20733	+	2.97856i	0.0842762	+	0.113722i
$687$	45.4860	−	5.78311i	1.73540	−	0.220639i
$688$	−7.65379	+	11.4178i	−0.291798	+	0.435298i
$689$		−	15.1366i		−	0.576658i
$690$		0			0
$691$	−23.0993			−0.878740			−0.439370	−	0.898306i	$-0.644798\pi$
$691$	−23.0993			−0.878740			−0.439370	+	0.898306i	$0.644798\pi$
$692$	−22.4749	−	6.83600i	−0.854367	−	0.259866i
$693$	13.8814	+	53.7084i	0.527311	+	2.04021i
$694$	−29.4612	−	39.7548i	−1.11833	−	1.50907i
$695$		0			0
$696$	2.35530	+	4.64876i	0.0892773	+	0.176211i
$697$			6.12753i			0.232097i
$698$	9.37375	−	6.94662i	0.354802	−	0.262934i
$699$	5.32534	+	41.8855i	0.201423	+	1.58426i
$700$		0			0
$701$	−0.254246			−0.00960274			−0.00480137	−	0.999988i	$-0.501528\pi$
$701$	−0.254246			−0.00960274			−0.00480137	+	0.999988i	$0.501528\pi$
$702$	−6.59137	+	10.6633i	−0.248775	+	0.402461i
$703$	9.56802			0.360865
$704$	−25.6811	−	31.4358i	−0.967893	−	1.18478i
$705$		0			0
$706$	0.787326	+	1.06241i	0.0296314	+	0.0399845i
$707$	37.0022			1.39161
$708$	−0.458805	+	2.69203i	−0.0172430	+	0.101173i
$709$		−	19.9746i		−	0.750163i	−0.926992	−	0.375082i	$-0.877615\pi$
$709$		−	19.9746i		−	0.750163i	0.926992	−	0.375082i	$-0.122385\pi$
$710$		0			0
$711$	−0.745342	−	2.88380i	−0.0279525	−	0.108151i
$712$	−10.9942	−	30.8355i	−0.412025	−	1.15561i
$713$	−22.8899			−0.857233
$714$	26.3002	−	25.2094i	0.984260	−	0.943438i
$715$		0			0
$716$	−0.893313	−	0.271712i	−0.0333847	−	0.0101543i
$717$	−1.19529	−	9.40133i	−0.0446389	−	0.351099i
$718$	27.4342	+	37.0195i	1.02383	+	1.38156i
$719$	−33.7978			−1.26044			−0.630222	−	0.776415i	$-0.717036\pi$
$719$	−33.7978			−1.26044			−0.630222	+	0.776415i	$0.717036\pi$
$720$		0			0
$721$	56.6317			2.10908
$722$	14.6526	+	19.7722i	0.545315	+	0.735846i
$723$	5.38374	+	42.3449i	0.200224	+	1.57482i
$724$	31.6920	+	9.63949i	1.17782	+	0.358249i
$725$		0			0
$726$	−26.0754	+	24.9939i	−0.967749	+	0.927612i
$727$	−27.0308			−1.00252			−0.501258	−	0.865298i	$-0.667129\pi$
$727$	−27.0308			−1.00252			−0.501258	+	0.865298i	$0.667129\pi$
$728$	16.5628	−	5.90534i	0.613857	−	0.218866i
$729$	−19.5934	+	18.5768i	−0.725682	+	0.688030i
$730$		0			0
$731$		−	14.0247i		−	0.518722i
$732$	0.365259	−	2.14315i	0.0135003	−	0.0792130i
$733$	−15.8811			−0.586583			−0.293291	−	0.956023i	$-0.594751\pi$
$733$	−15.8811			−0.586583			−0.293291	+	0.956023i	$0.594751\pi$
$734$	−0.666813	−	0.899795i	−0.0246125	−	0.0332121i
$735$		0			0
$736$	−26.5613	+	1.25519i	−0.979063	+	0.0462669i
$737$	21.2185			0.781592
$738$	−4.00593	+	4.95267i	−0.147460	+	0.182310i
$739$	14.1753			0.521446			0.260723	−	0.965414i	$-0.416039\pi$
$739$	14.1753			0.521446			0.260723	+	0.965414i	$0.416039\pi$
$740$		0			0
$741$	0.471140	+	3.70567i	0.0173078	+	0.136131i
$742$	−36.7398	+	27.2269i	−1.34876	+	0.999530i
$743$		−	29.5744i		−	1.08498i	−0.840063	−	0.542489i	$-0.817482\pi$
$743$		−	29.5744i		−	1.08498i	0.840063	−	0.542489i	$-0.182518\pi$
$744$	−21.2802	+	10.7816i	−0.780169	+	0.395273i
$745$		0			0
$746$	15.7740	+	21.2854i	0.577527	+	0.779313i
$747$	22.4390	−	5.79954i	0.820999	−	0.212194i
$748$	39.6236	+	12.0520i	1.44878	+	0.440665i
$749$	−54.1926			−1.98016
$750$		0			0
$751$			7.58573i			0.276807i	0.990376	+	0.138404i	$0.0441971\pi$
$751$			7.58573i			0.276807i	−0.990376	+	0.138404i	$0.955803\pi$
$752$	24.3161	−	36.2742i	0.886716	−	1.32278i
$753$	−3.00642	+	0.382237i	−0.109560	+	0.0139295i
$754$	−1.52804	−	2.06193i	−0.0556478	−	0.0750909i
$755$		0			0
$756$	37.7384	−	3.18187i	1.37253	−	0.115723i
$757$	−31.1258			−1.13129			−0.565643	−	0.824650i	$-0.691372\pi$
$757$	−31.1258			−1.13129			−0.565643	+	0.824650i	$0.691372\pi$
$758$	7.47921	+	10.0924i	0.271657	+	0.366573i
$759$	5.21043	+	40.9817i	0.189127	+	1.48754i
$760$		0			0
$761$		−	8.24575i		−	0.298908i	−0.988769	−	0.149454i	$-0.952248\pi$
$761$		−	8.24575i		−	0.298908i	0.988769	−	0.149454i	$-0.0477516\pi$
$762$	−9.95567	+	9.54275i	−0.360656	+	0.345697i
$763$			38.4017i			1.39024i
$764$	3.77780	−	12.4204i	0.136676	−	0.449353i
$765$		0			0
$766$	3.95880	−	2.93376i	0.143037	−	0.106001i
$767$		−	1.34484i		−	0.0485594i
$768$	−24.1022	+	13.6779i	−0.869713	+	0.493557i
$769$	26.3262			0.949347			0.474674	−	0.880162i	$-0.342566\pi$
$769$	26.3262			0.949347			0.474674	+	0.880162i	$0.342566\pi$
$770$		0			0
$771$	1.15267	+	9.06612i	0.0415124	+	0.326508i
$772$	21.8158	+	6.63555i	0.785169	+	0.238819i
$773$			27.2417i			0.979817i	0.871774	+	0.489909i	$0.162970\pi$
$773$			27.2417i			0.979817i	−0.871774	+	0.489909i	$0.837030\pi$
$774$	9.16878	−	11.3357i	0.329565	−	0.407452i
$775$		0			0
$776$	−7.03041	−	19.7183i	−0.252377	−	0.707845i
$777$	6.02518	+	47.3900i	0.216152	+	1.70011i
$778$	−20.8844	−	28.1813i	−0.748741	−	1.01035i
$779$			1.89812i			0.0680074i
$780$		0			0
$781$			31.5447i			1.12876i
$782$	21.7975	−	16.1535i	0.779478	−	0.577649i
$783$	−2.04711	−	5.13445i	−0.0731577	−	0.183490i
$784$	−20.8679	−	13.9886i	−0.745281	−	0.499592i
$785$		0			0
$786$	−2.81733	−	2.93923i	−0.100491	−	0.104839i
$787$		−	26.9324i		−	0.960037i	−0.877258	−	0.480019i	$-0.840630\pi$
$787$		−	26.9324i		−	0.960037i	0.877258	−	0.480019i	$-0.159370\pi$
$788$	6.81361	+	2.07244i	0.242725	+	0.0738277i
$789$	3.07636	−	0.391129i	0.109521	−	0.0139246i
$790$		0			0
$791$	−36.2369			−1.28843
$792$	24.1473	+	35.6455i	0.858036	+	1.26661i
$793$			1.07064i			0.0380195i
$794$	13.1249	+	17.7107i	0.465785	+	0.628528i
$795$		0			0
$796$	−8.42822	−	2.56354i	−0.298730	−	0.0908624i
$797$			13.1279i			0.465016i	0.972595	+	0.232508i	$0.0746931\pi$
$797$			13.1279i			0.465016i	−0.972595	+	0.232508i	$0.925307\pi$
$798$	8.14701	−	7.80911i	0.288401	−	0.276439i
$799$			44.5565i			1.57629i
$800$		0			0
$801$	8.68886	+	33.6180i	0.307006	+	1.18783i
$802$	29.9794	−	22.2169i	1.05861	−	0.784506i
$803$	21.3966			0.755071
$804$	2.43379	−	14.2802i	0.0858331	−	0.503624i
$805$		0			0
$806$	9.43868	−	6.99474i	0.332463	−	0.246379i
$807$	4.08685	+	32.1444i	0.143864	+	1.13154i
$808$	27.0506	−	9.64470i	0.951636	−	0.339299i
$809$		−	29.5632i		−	1.03939i	−0.854353	−	0.519693i	$-0.826046\pi$
$809$		−	29.5632i		−	1.03939i	0.854353	−	0.519693i	$-0.173954\pi$
$810$		0			0
$811$	29.2269			1.02629			0.513147	−	0.858301i	$-0.328480\pi$
$811$	29.2269			1.02629			0.513147	+	0.858301i	$0.328480\pi$
$812$	−2.25620	+	7.41776i	−0.0791772	+	0.260312i
$813$	42.6877	−	5.42733i	1.49712	−	0.190345i
$814$	−43.6329	+	32.3351i	−1.52933	+	1.13334i
$815$		0			0
$816$	12.6560	−	25.2846i	0.443048	−	0.885140i
$817$		−	4.34443i		−	0.151992i
$818$	−0.418605	−	0.564865i	−0.0146362	−	0.0197500i
$819$	−18.0573	+	4.66707i	−0.630973	+	0.163081i
$820$		0			0
$821$	5.29201			0.184692			0.0923462	−	0.995727i	$-0.470563\pi$
$821$	5.29201			0.184692			0.0923462	+	0.995727i	$0.470563\pi$
$822$	23.6168	−	22.6373i	0.823731	−	0.789567i
$823$	−16.0047			−0.557890			−0.278945	−	0.960307i	$-0.589985\pi$
$823$	−16.0047			−0.557890			−0.278945	+	0.960307i	$0.589985\pi$
$824$	41.4008	−	14.7612i	1.44227	−	0.514230i
$825$		0			0
$826$	−3.26422	+	2.41903i	−0.113577	+	0.0841687i
$827$	−4.13539			−0.143802			−0.0719009	−	0.997412i	$-0.522907\pi$
$827$	−4.13539			−0.143802			−0.0719009	+	0.997412i	$0.522907\pi$
$828$	28.1787	+	1.19400i	0.979277	+	0.0414943i
$829$			22.5879i			0.784512i	0.919856	+	0.392256i	$0.128305\pi$
$829$			22.5879i			0.784512i	−0.919856	+	0.392256i	$0.871695\pi$
$830$		0			0
$831$	−6.37954	−	50.1771i	−0.221304	−	1.74063i
$832$	10.5690	−	8.63424i	0.366415	−	0.299339i
$833$	25.6325			0.888113
$834$	−25.3826	+	24.3299i	−0.878929	+	0.842476i
$835$		0			0
$836$	12.2742	+	3.73335i	0.424512	+	0.129120i
$837$	23.5035	−	9.37084i	0.812399	−	0.323904i
$838$	−12.5257	+	9.28242i	−0.432692	+	0.320656i
$839$	32.0329			1.10590			0.552949	−	0.833215i	$-0.313502\pi$
$839$	32.0329			1.10590			0.552949	+	0.833215i	$0.313502\pi$
$840$		0			0
$841$	−27.8684			−0.960979
$842$	12.6088	−	9.34402i	0.434527	−	0.322016i
$843$	39.4944	−	5.02133i	1.36026	−	0.172944i
$844$	9.39176	−	30.8775i	0.323278	−	1.06285i
$845$		0			0
$846$	−29.1292	+	36.0134i	−1.00148	+	1.23817i
$847$	−53.7374			−1.84644
$848$	−19.7621	+	29.4806i	−0.678632	+	1.01237i
$849$	−3.49677	+	0.444581i	−0.120009	+	0.0152580i
$850$		0			0
$851$			35.5760i			1.21953i
$852$	21.2298	+	3.61822i	0.727322	+	0.123958i
$853$	−10.3607			−0.354745			−0.177372	−	0.984144i	$-0.556760\pi$
$853$	−10.3607			−0.354745			−0.177372	+	0.984144i	$0.556760\pi$
$854$	2.59867	−	1.92581i	0.0889248	−	0.0658997i
$855$		0			0
$856$	−39.6177	+	14.1254i	−1.35411	+	0.482797i
$857$	−18.1893			−0.621334			−0.310667	−	0.950519i	$-0.600552\pi$
$857$	−18.1893			−0.621334			−0.310667	+	0.950519i	$0.600552\pi$
$858$	−14.6718	−	15.3067i	−0.500888	−	0.522561i
$859$	−27.2650			−0.930271			−0.465136	−	0.885239i	$-0.653994\pi$
$859$	−27.2650			−0.930271			−0.465136	+	0.885239i	$0.653994\pi$
$860$		0			0
$861$	−9.40133	+	1.19529i	−0.320396	+	0.0407353i
$862$	−5.75943	−	7.77176i	−0.196167	−	0.264707i
$863$			12.4082i			0.422381i	0.977445	+	0.211191i	$0.0677341\pi$
$863$			12.4082i			0.422381i	−0.977445	+	0.211191i	$0.932266\pi$
$864$	26.7595	−	12.1627i	0.910375	−	0.413784i
$865$		0			0
$866$	43.9011	−	32.5338i	1.49182	−	1.10555i
$867$	−0.0751522	−	0.591096i	−0.00255230	−	0.0200747i
$868$	−33.9556	−	10.3280i	−1.15253	−	0.350555i
$869$	5.03776			0.170894
$870$		0			0
$871$			7.13386i			0.241722i
$872$	10.0095	+	28.0737i	0.338964	+	0.950697i
$873$	5.55623	+	21.4976i	0.188050	+	0.727582i
$874$	6.75221	−	5.00388i	0.228397	−	0.169259i
$875$		0			0
$876$	2.45422	−	14.4001i	0.0829205	−	0.486535i
$877$	−9.19349			−0.310442			−0.155221	−	0.987880i	$-0.549609\pi$
$877$	−9.19349			−0.310442			−0.155221	+	0.987880i	$0.549609\pi$
$878$	4.63474	−	3.43468i	0.156415	−	0.115915i
$879$	−10.3093	+	1.31073i	−0.347725	+	0.0442098i
$880$		0			0
$881$		−	38.4479i		−	1.29534i	−0.761920	−	0.647671i	$-0.775743\pi$
$881$		−	38.4479i		−	1.29534i	0.761920	−	0.647671i	$-0.224257\pi$
$882$	20.7178	+	16.7575i	0.697605	+	0.564253i
$883$		−	5.12406i		−	0.172438i	−0.996276	−	0.0862192i	$-0.972521\pi$
$883$		−	5.12406i		−	0.172438i	0.996276	−	0.0862192i	$-0.0274785\pi$
$884$	−4.05201	+	13.3219i	−0.136284	+	0.448063i
$885$		0			0
$886$	−10.7054	−	14.4459i	−0.359656	−	0.485319i
$887$		−	1.79043i		−	0.0601169i	−0.999548	−	0.0300584i	$-0.990431\pi$
$887$		−	1.79043i		−	0.0601169i	0.999548	−	0.0300584i	$-0.00956934\pi$
$888$	16.7570	+	33.0742i	0.562329	+	1.10990i
$889$	−20.5171			−0.688121
$890$		0			0
$891$	−22.1275	−	39.9472i	−0.741300	−	1.33828i
$892$	3.54713	−	11.6620i	0.118767	−	0.390471i
$893$			13.8022i			0.461874i
$894$	−32.3149	+	30.9746i	−1.08077	+	1.03595i
$895$		0			0
$896$	−39.9682	−	10.1226i	−1.33524	−	0.338171i
$897$	−13.7785	+	1.75180i	−0.460050	+	0.0584909i
$898$	35.5620	−	26.3540i	1.18672	−	0.879444i
$899$			5.18002i			0.172763i
$900$		0			0
$901$		−	36.2118i		−	1.20639i
$902$	−6.41471	−	8.65598i	−0.213586	−	0.288213i
$903$	21.5178	−	2.73578i	0.716066	−	0.0910409i
$904$	−26.4911	+	9.44522i	−0.881081	+	0.314143i
$905$		0			0
$906$	−28.4169	−	29.6465i	−0.944087	−	0.984938i
$907$			34.5506i			1.14724i	0.819123	+	0.573618i	$0.194460\pi$
$907$			34.5506i			1.14724i	−0.819123	+	0.573618i	$0.805540\pi$
$908$	11.9119	−	39.1630i	0.395311	−	1.29967i
$909$	−29.4915	+	7.62234i	−0.978172	+	0.252817i
$910$		0			0
$911$	52.6515			1.74442			0.872211	−	0.489130i	$-0.162686\pi$
$911$	52.6515			1.74442			0.872211	+	0.489130i	$0.162686\pi$
$912$	3.92044	−	7.83242i	0.129819	−	0.259357i
$913$			39.1991i			1.29730i
$914$	33.0751	−	24.5110i	1.09403	−	0.810753i
$915$		0			0
$916$	50.6542	+	15.4071i	1.67366	+	0.509064i
$917$		−	6.05731i		−	0.200030i
$918$	−15.7688	+	25.5102i	−0.520446	+	0.841962i
$919$			13.0595i			0.430794i	0.976527	+	0.215397i	$0.0691046\pi$
$919$			13.0595i			0.430794i	−0.976527	+	0.215397i	$0.930895\pi$
$920$		0			0
$921$	−32.7401	+	4.16259i	−1.07882	+	0.137162i
$922$	−0.00578529	−	0.00780665i	−0.000190528	−	0.000257098i
$923$	−10.6056			−0.349089
$924$	−10.7618	+	63.1445i	−0.354037	+	2.07730i
$925$		0			0
$926$	−15.1483	−	20.4411i	−0.497805	−	0.671737i
$927$	−45.1367	+	11.6660i	−1.48248	+	0.383160i
$928$	0.284051	+	6.01087i	0.00932444	+	0.197316i
$929$		−	20.9794i		−	0.688313i	−0.938912	−	0.344156i	$-0.888165\pi$
$929$		−	20.9794i		−	0.688313i	0.938912	−	0.344156i	$-0.111835\pi$
$930$		0			0
$931$	7.94016			0.260228
$932$	−14.1875	+	46.6446i	−0.464728	+	1.52790i
$933$	−5.69953	−	44.8287i	−0.186594	−	1.46762i
$934$	3.36748	+	4.54406i	0.110187	+	0.148686i
$935$		0			0
$936$	−11.9844	+	8.11856i	−0.391722	+	0.265363i
$937$			5.78393i			0.188953i	0.995527	+	0.0944764i	$0.0301177\pi$
$937$			5.78393i			0.188953i	−0.995527	+	0.0944764i	$0.969882\pi$
$938$	17.3155	−	12.8320i	0.565370	−	0.418980i
$939$	34.6729	−	4.40832i	1.13151	−	0.143860i
$940$		0			0
$941$	42.0131			1.36959			0.684794	−	0.728737i	$-0.259892\pi$
$941$	42.0131			1.36959			0.684794	+	0.728737i	$0.259892\pi$
$942$	11.1637	−	10.7007i	0.363732	−	0.348646i
$943$	−7.05764			−0.229829
$944$	−1.75580	+	2.61927i	−0.0571464	+	0.0852498i
$945$		0			0
$946$	14.6820	+	19.8118i	0.477353	+	0.644138i
$947$	−23.5854			−0.766421			−0.383211	−	0.923661i	$-0.625182\pi$
$947$	−23.5854			−0.766421			−0.383211	+	0.923661i	$0.625182\pi$
$948$	0.577838	−	3.39046i	0.0187673	−	0.110117i
$949$			7.19377i			0.233520i
$950$		0			0
$951$	13.4296	−	1.70744i	0.435484	−	0.0553675i
$952$	39.6236	−	14.1275i	1.28421	−	0.457876i
$953$	31.8648			1.03220			0.516102	−	0.856527i	$-0.327383\pi$
$953$	31.8648			1.03220			0.516102	+	0.856527i	$0.327383\pi$
$954$	23.6738	−	29.2687i	0.766467	−	0.947609i
$955$		0			0
$956$	3.18443	−	10.4695i	0.102992	−	0.338609i
$957$	9.27423	−	1.17913i	0.299793	−	0.0381159i
$958$	28.7522	+	38.7982i	0.928943	+	1.25351i
$959$	48.6706			1.57166
$960$		0			0
$961$	7.28794			0.235095
$962$	−10.8714	−	14.6698i	−0.350508	−	0.472974i
$963$	43.1927	−	11.1635i	1.39186	−	0.359739i
$964$	−14.3431	+	47.1562i	−0.461961	+	1.51880i
$965$		0			0
$966$	29.0360	+	30.2924i	0.934217	+	0.974641i
$967$	11.1038			0.357073			0.178537	−	0.983933i	$-0.442864\pi$
$967$	11.1038			0.357073			0.178537	+	0.983933i	$0.442864\pi$
$968$	−39.2850	+	14.0068i	−1.26267	+	0.450195i
$969$	1.12712	+	8.86519i	0.0362084	+	0.284791i
$970$		0			0
$971$		−	47.5500i		−	1.52595i	−0.646427	−	0.762976i	$-0.723737\pi$
$971$		−	47.5500i		−	1.52595i	0.646427	−	0.762976i	$-0.276263\pi$
$972$	−29.4228	+	10.3100i	−0.943738	+	0.330694i
$973$	−52.3097			−1.67697
$974$	−0.717251	−	0.967856i	−0.0229822	−	0.0310121i
$975$		0			0
$976$	1.39781	−	2.08522i	0.0447427	−	0.0667462i
$977$	51.9896			1.66329			0.831647	−	0.555304i	$-0.187398\pi$
$977$	51.9896			1.66329			0.831647	+	0.555304i	$0.187398\pi$
$978$	−4.56139	−	4.75876i	−0.145857	−	0.152168i
$979$	−58.7279			−1.87695
$980$		0			0
$981$	−7.91064	−	30.6070i	−0.252567	−	0.977206i
$982$	6.92090	−	5.12888i	0.220855	−	0.163669i
$983$			27.4842i			0.876609i	0.898826	+	0.438305i	$0.144421\pi$
$983$			27.4842i			0.876609i	−0.898826	+	0.438305i	$0.855579\pi$
$984$	−6.56132	+	3.32430i	−0.209167	+	0.105975i
$985$		0			0
$986$	−3.65557	−	4.93281i	−0.116417	−	0.157093i
$987$	−68.3619	+	8.69155i	−2.17598	+	0.276655i
$988$	−1.25519	+	4.12671i	−0.0399329	+	0.131288i
$989$	16.1535			0.513653
$990$		0			0
$991$			24.4556i			0.776858i	0.921479	+	0.388429i	$0.126982\pi$
$991$			24.4556i			0.776858i	−0.921479	+	0.388429i	$0.873018\pi$
$992$	−27.5154	+	1.30027i	−0.873614	+	0.0412837i
$993$	−2.19382	−	17.2551i	−0.0696188	−	0.547575i
$994$	19.0769	+	25.7422i	0.605081	+	0.816494i
$995$		0			0
$996$	26.3813	+	4.49619i	0.835924	+	0.142467i
$997$	−39.1729			−1.24062			−0.620309	−	0.784358i	$-0.712993\pi$
$997$	−39.1729			−1.24062			−0.620309	+	0.784358i	$0.712993\pi$
$998$	11.0621	+	14.9271i	0.350164	+	0.472510i
$999$	−14.5644	−	36.5296i	−0.460797	−	1.15575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.d.299.5		16
3.2	odd	2		600.2.m.c.299.12		16
4.3	odd	2		2400.2.m.c.1199.7		16
5.2	odd	4		600.2.b.e.251.7		8
5.3	odd	4		120.2.b.b.11.2	yes	8
5.4	even	2	inner	600.2.m.d.299.12		16
8.3	odd	2		600.2.m.c.299.6		16
8.5	even	2		2400.2.m.d.1199.7		16
12.11	even	2		2400.2.m.d.1199.9		16
15.2	even	4		600.2.b.f.251.2		8
15.8	even	4		120.2.b.a.11.7	✓	8
15.14	odd	2		600.2.m.c.299.5		16
20.3	even	4		480.2.b.a.431.7		8
20.7	even	4		2400.2.b.e.2351.2		8
20.19	odd	2		2400.2.m.c.1199.10		16
24.5	odd	2		2400.2.m.c.1199.9		16
24.11	even	2	inner	600.2.m.d.299.11		16
40.3	even	4		120.2.b.a.11.8	yes	8
40.13	odd	4		480.2.b.b.431.7		8
40.19	odd	2		600.2.m.c.299.11		16
40.27	even	4		600.2.b.f.251.1		8
40.29	even	2		2400.2.m.d.1199.10		16
40.37	odd	4		2400.2.b.f.2351.2		8
60.23	odd	4		480.2.b.b.431.8		8
60.47	odd	4		2400.2.b.f.2351.1		8
60.59	even	2		2400.2.m.d.1199.8		16
120.29	odd	2		2400.2.m.c.1199.8		16
120.53	even	4		480.2.b.a.431.8		8
120.59	even	2	inner	600.2.m.d.299.6		16
120.77	even	4		2400.2.b.e.2351.1		8
120.83	odd	4		120.2.b.b.11.1	yes	8
120.107	odd	4		600.2.b.e.251.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.7	✓	8	15.8	even	4
120.2.b.a.11.8	yes	8	40.3	even	4
120.2.b.b.11.1	yes	8	120.83	odd	4
120.2.b.b.11.2	yes	8	5.3	odd	4
480.2.b.a.431.7		8	20.3	even	4
480.2.b.a.431.8		8	120.53	even	4
480.2.b.b.431.7		8	40.13	odd	4
480.2.b.b.431.8		8	60.23	odd	4
600.2.b.e.251.7		8	5.2	odd	4
600.2.b.e.251.8		8	120.107	odd	4
600.2.b.f.251.1		8	40.27	even	4
600.2.b.f.251.2		8	15.2	even	4
600.2.m.c.299.5		16	15.14	odd	2
600.2.m.c.299.6		16	8.3	odd	2
600.2.m.c.299.11		16	40.19	odd	2
600.2.m.c.299.12		16	3.2	odd	2
600.2.m.d.299.5		16	1.1	even	1	trivial
600.2.m.d.299.6		16	120.59	even	2	inner
600.2.m.d.299.11		16	24.11	even	2	inner
600.2.m.d.299.12		16	5.4	even	2	inner
2400.2.b.e.2351.1		8	120.77	even	4
2400.2.b.e.2351.2		8	20.7	even	4
2400.2.b.f.2351.1		8	60.47	odd	4
2400.2.b.f.2351.2		8	40.37	odd	4
2400.2.m.c.1199.7		16	4.3	odd	2
2400.2.m.c.1199.8		16	120.29	odd	2
2400.2.m.c.1199.9		16	24.5	odd	2
2400.2.m.c.1199.10		16	20.19	odd	2
2400.2.m.d.1199.7		16	8.5	even	2
2400.2.m.d.1199.8		16	60.59	even	2
2400.2.m.d.1199.9		16	12.11	even	2
2400.2.m.d.1199.10		16	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.842022 - 1.13622i) q^{2} +(0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(1.76833 - 1.69499i) q^{6} +3.64426 q^{7} +(2.66415 - 0.949886i) q^{8} +(-2.90455 + 0.750707i) q^{9} +O(q^{10})\)	\(q+(-0.842022 - 1.13622i) q^{2} +(0.218455 + 1.71822i) q^{3} +(-0.581998 + 1.91345i) q^{4} +(1.76833 - 1.69499i) q^{6} +3.64426 q^{7} +(2.66415 - 0.949886i) q^{8} +(-2.90455 + 0.750707i) q^{9} -5.07403i q^{11} +(-3.41486 - 0.581998i) q^{12} +1.70594 q^{13} +(-3.06855 - 4.14069i) q^{14} +(-3.32256 - 2.22724i) q^{16} +4.08117 q^{17} +(3.29867 + 2.66811i) q^{18} +1.26422 q^{19} +(0.796108 + 6.26164i) q^{21} +(-5.76522 + 4.27244i) q^{22} +4.70066i q^{23} +(2.21411 + 4.37009i) q^{24} +(-1.43644 - 1.93832i) q^{26} +(-1.92439 - 4.82667i) q^{27} +(-2.12095 + 6.97311i) q^{28} +1.06377 q^{29} +4.86950i q^{31} +(0.267024 + 5.65055i) q^{32} +(8.71829 - 1.10845i) q^{33} +(-3.43644 - 4.63712i) q^{34} +(0.254006 - 5.99462i) q^{36} +7.56830 q^{37} +(-1.06450 - 1.43644i) q^{38} +(0.372671 + 2.93118i) q^{39} +1.50141i q^{41} +(6.44427 - 6.17700i) q^{42} -3.43644i q^{43} +(9.70888 + 2.95307i) q^{44} +(5.34099 - 3.95806i) q^{46} +10.9176i q^{47} +(3.10106 - 6.19543i) q^{48} +6.28066 q^{49} +(0.891553 + 7.01235i) q^{51} +(-0.992853 + 3.26422i) q^{52} -8.87288i q^{53} +(-3.86378 + 6.25070i) q^{54} +(9.70888 - 3.46163i) q^{56} +(0.276176 + 2.17221i) q^{57} +(-0.895716 - 1.20868i) q^{58} -0.788328i q^{59} +0.627594i q^{61} +(5.53283 - 4.10023i) q^{62} +(-10.5850 + 2.73578i) q^{63} +(6.19543 - 5.06128i) q^{64} +(-8.60043 - 8.97257i) q^{66} +4.18178i q^{67} +(-2.37523 + 7.80911i) q^{68} +(-8.07677 + 1.02688i) q^{69} -6.21689 q^{71} +(-7.02510 + 4.75900i) q^{72} +4.21689i q^{73} +(-6.37267 - 8.59926i) q^{74} +(-0.735776 + 2.41903i) q^{76} -18.4911i q^{77} +(3.01667 - 2.89155i) q^{78} +0.992853i q^{79} +(7.87288 - 4.36094i) q^{81} +(1.70594 - 1.26422i) q^{82} -7.72544 q^{83} +(-12.4447 - 2.12095i) q^{84} +(-3.90455 + 2.89356i) q^{86} +(0.232385 + 1.82779i) q^{87} +(-4.81975 - 13.5180i) q^{88} -11.5742i q^{89} +6.21689 q^{91} +(-8.99447 - 2.73578i) q^{92} +(-8.36687 + 1.06377i) q^{93} +(12.4048 - 9.19282i) q^{94} +(-9.65055 + 1.69320i) q^{96} -7.40133i q^{97} +(-5.28845 - 7.13622i) q^{98} +(3.80911 + 14.7378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 2 q^{6}+O(q^{10}) \) 16 * q - 2 * q^4 + 2 * q^6	\( 16 q - 2 q^{4} + 2 q^{6} + 12 q^{14} - 14 q^{16} + 8 q^{19} - 8 q^{21} + 22 q^{24} + 32 q^{26} + 26 q^{36} - 32 q^{39} + 60 q^{44} - 16 q^{46} + 32 q^{49} + 40 q^{51} - 82 q^{54} + 60 q^{56} - 50 q^{64} - 68 q^{66} - 40 q^{69} - 48 q^{71} - 64 q^{74} - 24 q^{76} + 16 q^{81} - 116 q^{84} - 16 q^{86} + 48 q^{91} + 80 q^{94} - 86 q^{96} - 32 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 + 2 * q^6 + 12 * q^14 - 14 * q^16 + 8 * q^19 - 8 * q^21 + 22 * q^24 + 32 * q^26 + 26 * q^36 - 32 * q^39 + 60 * q^44 - 16 * q^46 + 32 * q^49 + 40 * q^51 - 82 * q^54 + 60 * q^56 - 50 * q^64 - 68 * q^66 - 40 * q^69 - 48 * q^71 - 64 * q^74 - 24 * q^76 + 16 * q^81 - 116 * q^84 - 16 * q^86 + 48 * q^91 + 80 * q^94 - 86 * q^96 - 32 * q^99

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